Math ImageryThe connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.

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Home > Chaim Goodman-Strauss :: Symmetries
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"The Hexacosm," by Chaim Goodman-Strauss, University of Arkansas (

This spaceship is flying about in the universal cover of the hexacosm, one of the ten, closed, flat three-manifolds. Equivalently, the pattern is one of the ten discrete co-compact symmetry types of Euclidean space that does not have any fixed points. The type here is (6_1 3_1 2_1) in the Thurston-Conway fibrefold notation. This image is from "The Symmetries of Things", by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss (AK Peters, 2008).

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American Mathematical Society